The research was published on August 24 to coincide with the launch of the Irish Redhead Convention in Crosshaven, County Cork, which comes a week after a “ginger pride” march in Edinburgh and will be followed by a redhead convention in Breda, Holland, next weekend.

The study by BritainsDNA suggests there is a “vast army of secret carriers”, which is likely to include some of those who are guilty of “ginger bashing”.

Both parents have to have one of the gene variants to produce red haired offspring, which means that generations of families can have no redheads before apparently producing a redheaded child “out of nowhere”.

The biggest study of redhead genetics in the UK was based on ancestral data from more than 2,300 people who have undergone DNA tests to learn more about their ancestry.

Alistair Moffat, managing director of BritainsDNA, and a former director of the Edinburgh Fringe Festival, said: “No-one needs a DNA test to tell if they have red hair. All they need is a mirror. What BritainsDNA set out to discover was a hidden story, the story of the secret carriers.

“Since red hair is recessive, children born with red hair need both parents to be carriers of one of the red hair gene variants, but millions of people in Britain and Ireland have no idea that they are carriers. The project reveals just how red headed a nation we really are.

“If both parents are carriers of a red hair gene variant, there is a 25 per cent change their offspring will have red hair.”

Around six per cent of Scots have red hair, about 300,000 people, and 4 per cent of English people, with a concentration in the north of England.

The group estimated that out of the UK and Irish population of around 67 million, about 20.4 million people carry one of the three most prominent red haired gene variants.

Dr Jim Wilson, the company’s chief scientific officer, a geneticist at Edinburgh University, said he was most surprised to learn that the Lothian and Borders were the most red headed area in the country, and not Scotland’s far flung islands.

He said the lower percentages for the gene variants in the south of England and the far north of Scotland suggested that Anglo Saxons diluted the red headed gene in England, and Norse Vikings diluted it in the north and west of Scotland.